![]() The method of proof should be listed in a series of statements, which are each justified by the given information, a definition, and either a postulate or an already-proven theorem. Once all of the data has been gleaned from the initial claim, given information and any diagrams, constructing the proof begins with stating the hypothesis and the given information. Symbols of equality, right angles and angle measures given in a diagram can be used as statements in a proof. Some proofs will present an initial diagram that may be used for given information. Examples of common postulates are the reflexive property of equality, the symmetric property of equality and the transitive property of equality. Reviewing postulates and identifying their place in a proof is another step in reasoning to prove an initial claim. Postulates are accepted without proof and are statements that can be used as reasons in a proof. Theorems are statements that have been proven through the process of deductive reasoning and can be used to support other claims. Additionally, there may be theorems that are relevant to the proof. For example, if the proof involves an isosceles triangle, noting the definition and characteristics of the special triangle can form a basis for your investigation. If the given information involves a geometric term that can be defined, make a note of it. The given statement may be broken into terms that can be defined. Every proof will begin with a given statement, a fact given as a first step to proving another statement.
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